Congruences and Hoehnke radicals on graphs

On Simple Graphs Arising from Exponential Congruences

We introduce and investigate a new class of graphs arrived from exponential congruences. For each pair of positive integers a and b, let G n denote the graph for which V {0, 1, . . . , n − 1} is the set of vertices and there is an edge between a and b if the congruence a ≡ b modn is solvable. Let n p1 1 p k2 2 · · · pr r be the prime power factorization of an integer n, where p1 < p2 < · · · < ...

On congruences of automata defined by directed graphs

Graphs and various objects derived from them are basic essential tools that have been actively used in various branches of modern theoretical computer science. In particular, graph grammars and graph transformations have been very well explored in the literature. We consider finite state automata defined by directed graphs, characterize all their congruences, and give a complete description of ...

Mal’cev Conditions from Graphs for Congruences and Tolerances

In [L4] we showed that, under certain conditions, a variety satisfies a given congruence identity if and only if it satisfies the same tolerance identity. Moreover, we mentioned that a parallel result holds for Mal’cev conditions arising from graphs. In the present note we give detailed definitions and state these more general results. The motivating example for our constructions is the followi...

Tile Bisimilarity Congruences for Open Terms and Term Graphs

Fuzzy order congruences on fuzzy posets

Fuzzy order congruences play an important role in studying the categoricalproperties of fuzzy posets. In this paper, the correspondence between the fuzzyorder congruences and the fuzzy order-preserving maps is discussed. We focus onthe characterization of fuzzy order congruences on the fuzzy poset in terms ofthe fuzzy preorders containing the fuzzy partial order. At last, fuzzy completecongruen...